Graph Theory DM

Question

In this graph it is said that $a,e,b,c,b$ is a path. But according to definition- in a path vertices and edges can't repeat so why this is a path. confused please clarify.

Answer 1

There is No universally accepted definition of These Terms : Walk, Trail and Path.

So, It depends on How the Author has defined these terms. Every Author first describes/defines these terms and then Builds the concepts around these definitions.

For Example, If you refer Kenneth Rosen (Relation chapter)..He has describes Path as some authors define Walk. 

Hence, There is considerable variation of terminology concerning these concepts.

Some books defined like this :

Walk = Repetition of vertices and edges allowed.
Trail = Repetition of edges NOT allowed.
Path = Repetition of Vertices and Edges NOT allowed.

Other books define Walk as Path (From the above definitions) And Trail as Simple Path etc.

Because of these variations in terminology, you will need to make sure which set of definitions are used in a particular book or article. 

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Coming to GATE, If You scan previous GATE questions, They define these terms wherever conflict may occur.